In horse racing, a horse is carted away from the track because it couldn't finish the race due to injury and is unable to walk on its own.

For humans:

To be physically carried from a bar or party by friends, bouncers, local authorities, and/or random people because of great intoxication and the inability to walk. Person is then placed into a vehicle and driven away.

To be taken away in a police van from a party, bar, or for general hell raising.